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The mediation formula for the identification of natural (in)direct effects has facilitated mediation analyses that better respect the nature of the data, with greater consideration of the need for confounding control. The default assumptions on which it relies are strong, however. In particular, they are known to be violated when confounders of the mediator–outcome association are affected by the exposure. This complicates extensions of counterfactual-based mediation analysis to settings that involve repeatedly measured mediators, or multiple correlated mediators. VanderWeele, Vansteelandt, and Robins introduced so-called interventional (in)direct effects. These can be identified under much weaker conditions than natural (in)direct effects, but have the drawback of not adding up to the total effect. In this article, we adapt their proposal to achieve an exact decomposition of the total effect, and extend it to the multiple mediator setting. Interestingly, the proposed effects capture the path-specific effects of an exposure on an outcome that are mediated by distinct mediators, even when—as often—the structural dependence between the multiple mediators is unknown, for instance, when the direction of the causal effects between the mediators is unknown, or there may be unmeasured common causes of the mediators.

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From the aDepartment of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium; and bDepartment of Medical Statistics and Centre for Statistical Methodology, London School of Hygiene and Tropical Medicine, London, United Kingdom.

Submitted 18 January 2016; accepted 20 November 2016.

S.V.’s study was funded by the Fund for Scientific Research, Flanders (Belgium) (Grant 3G011112). R.M.D. was supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant 107617/Z/15/Z). The LSHTM Centre for Statistical Methodology is supported by the Wellcome Trust Institutional Strategic Support Fund, 097834/Z/11/B. Computing code is available in eAppendix D (http://links.lww.com/EDE/B146). Data are not available in open access.

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